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Isotopies of Legendrian 1-knots and Legendrian 2-tori
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. (Algebra, geometri, logik)
University of Tokyo, Graduate School of Mathematical Sciences.
2008 (English)In: The Journal of Symplectic Geometry, ISSN 1527-5256, E-ISSN 1540-2347, Vol. 6, no 4, 407-460 p.Article in journal (Refereed) Published
Abstract [en]

We construct a Legendrian 2-torus in the 1-jet space of S1 × R (orof R2) from a loop of Legendrian knots in the 1-jet space of R. The differential graded algebra (DGA) for the Legendrian contact homologyof the torus is explicitly computed in terms of the DGA of the knot and the monodromy operator of the loop. The contact homology of the torus is shown to depend only on the chain homotopy type of the monodromy operator. The construction leads to many new examples of Legendrian knotted tori. In particular, it allows us to construct a Legendrian torus with DGA which does not admit any augmentation(linearization) but which still has non-trivial homology, as well as two Legendrian tori with isomorphic linearized contact homologies but with distinct contact homologies.

Place, publisher, year, edition, pages
2008. Vol. 6, no 4, 407-460 p.
National Category
URN: urn:nbn:se:uu:diva-87225ISI: 000263416800003OAI: oai:DiVA.org:uu-87225DiVA: diva2:25575
Available from: 2008-12-02 Created: 2008-09-30 Last updated: 2010-09-13Bibliographically approved

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